Multiple-Choice Questions
1. [2 marks] Let . Evaluate . In other words, find the derivative of at .

(a) (b) (c) (d)

2. [2 marks] Let . Evaluate . In other words, find the second derivative of at .

(a) (b) (c) (d)

3. [2 marks] Let . Calculate

(a) (b) This limit does not exist (c) (d)

4. [2 marks] Evaluate the following limit: .

(a) (b) (c) (d)

5. [2 marks] A differentiable function has the property that , and . What is the value of the derivative of at ?

(a) (b) (c) (d)

6. [2 marks] Let . Evaluate . In other words, find the derivative of at .

(a) (b) (c) (d)

7. [2 marks] Let y be given implicitly as a differentiable function of by . Then the slope of the tangent line to the curve at the point where , is equal to:

(a) , (b) , (c) , (d) .

8. [2 marks] Let . Evaluate . In other words, find the derivative of at .

(a) (b) (c) (d)

9. [2 marks] Let . Calculate in the case where is a point where .

(a) (b) (c) (d) None of these

10. [2 marks] Evaluate using any method.

(a) (b) (c) (d)

11. [2 marks] Evaluate

(a)
(b)
(c) This limit does not exist (d)

12. [2 marks] Which of the following functions represents the form of the inverse function of the function whose domain is the set of all real numbers where .

(a) where
(b) where
(c) where
(d)

13. [2 marks] Solve the inequality for .

(a)
(b)
(c)
(d)

14. Determine an interval where the graph of the function defined by the polynomial is concave up.

(a)
(b)
(c)
(d)

15. [2 marks] Which of the following functions has a point of inflection at ?

(a)
(b)
(c)
(d)

16. [2 marks] For what values of is the function increasing?

(a)
(b)
(c)
(d)

17. [2 marks] Find all the critical points of

(a)
(b)
(c)
(d)

18. [2 marks] An antiderivative of is given by

(a)
(b)
(c)
(d)

19. [2 marks] Evaluate

(a)
(b)
(c)
(d)

20. [2 marks] Evaluate

(a)
(b)
(c)
(d)

21. [2 marks] The value of is

(a)
(b)
(c)
(d)

22. [2 marks] The most general antiderivative of is given by

(a)
(b)
(c)
(d)

23. [2 marks] Evaluate and simplify the indefinite integral: .

(a)
(b)
(c)
(d)

24. [2 marks] Evaluate the improper integral .

(a)
(b)
(c)
(d)

25. [2 marks] The form of the partial fraction decomposition of the rational function

is

(a)
(b)
(c)
(d)
where are constants to be determined.

26. [2 marks] Evaluate the indefinite trigonometric integral

(a)
(b)
(c)
(d)
where are constants to be determined.

27. [2 marks] The area enclosed by the intersection of the two curves defined by and is given by which of the following definite integrals?

(a)
(b)
(c)
(d)

28. [2 marks] Which of the following expressions gives the volume of the solid of revolution obtained when the region bounded by the graphs of and is revolved about the axis?

(a)
(b)
(c)
(d)

29. [2 marks] The center of mass of a thin quarter circle of radius having uniform density and situated in the first quadrant is given by which of the following points?

(a)
(b)
(c)
(d)

30. [2 marks] The general solution of the differential equation

is given by,

(a)
(b)
(c) (d)

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